Assume that

x_(1)

and

x_(2)

are independent normal random variables,

x_(i)N(\\\\mu ,\\\\sigma ^(2))

, and let\

Y_(1)=x_(1)+x_(2)

and

Y_(2)=x_(1)-x_(2)

. Show that

Y_(1)

and

Y_(2)

are independent and normally\ distributed.

9. Assume that X1 and X2 are independent normal random variables, XiN(,2), and let Y1=X1+X2 and Y2=X1X2. Show that Y1 and Y2 are independent and normally distributed